* [misc]progress: [Phase 1 of 3] Setting up. * * * [misc]progress: [1/2] Preparing points * * * [misc]progress: [2/2] Setting up program. * [enter]simplify: Simplifying (log (sqrt (+ (* re re) (* im im)))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (11 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * [exit]simplify: Simplified to (log (hypot im re)) * [misc]progress: [Phase 2 of 3] Improving. * * [misc]progress: iteration 1 / 2 * * * [misc]progress: picking best candidate * * * * [misc]pick: Picked # * * * [misc]progress: localizing error * * * [misc]progress: generating series expansions * * * * [misc]progress: [ 1 / 1 ] generating series at (2) * [misc]approximate: Taking taylor expansion of (log (hypot im re)) in (im re) around 0 * [misc]taylor: Taking taylor expansion of (log (hypot im re)) in re * [misc]taylor: Taking taylor expansion of (hypot im re) in re * [misc]backup-simplify: Simplify (hypot im re) into (hypot im re) * [misc]backup-simplify: Simplify (log (hypot im re)) into (log (hypot im re)) * [misc]taylor: Taking taylor expansion of (log (hypot im re)) in im * [misc]taylor: Taking taylor expansion of (hypot im re) in im * [misc]backup-simplify: Simplify (hypot im re) into (hypot im re) * [misc]backup-simplify: Simplify (log (hypot im re)) into (log (hypot im re)) * [misc]taylor: Taking taylor expansion of (log (hypot im re)) in im * [misc]taylor: Taking taylor expansion of (hypot im re) in im * [misc]backup-simplify: Simplify (hypot im re) into (hypot im re) * [misc]backup-simplify: Simplify (log (hypot im re)) into (log (hypot im re)) * [misc]taylor: Taking taylor expansion of (log (hypot im re)) in re * [misc]taylor: Taking taylor expansion of (hypot im re) in re * [misc]backup-simplify: Simplify (hypot im re) into (hypot im re) * [misc]backup-simplify: Simplify (log (hypot im re)) into (log (hypot im re)) * [misc]backup-simplify: Simplify (log (hypot im re)) into (log (hypot im re)) * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (hypot im re) 1)))) 1) into 0 * [misc]taylor: Taking taylor expansion of 0 in re * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (hypot im re) 1)))) 1) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (hypot im re) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (hypot im re) 1)))) 2) into 0 * [misc]taylor: Taking taylor expansion of 0 in re * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (hypot im re) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (hypot im re) 1)))) 2) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (hypot im re) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (hypot im re) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (hypot im re) 1)))) 6) into 0 * [misc]taylor: Taking taylor expansion of 0 in re * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (log (hypot im re)) into (log (hypot im re)) * [misc]approximate: Taking taylor expansion of (log (hypot (/ 1 im) (/ 1 re))) in (im re) around 0 * [misc]taylor: Taking taylor expansion of (log (hypot (/ 1 im) (/ 1 re))) in re * [misc]taylor: Taking taylor expansion of (hypot (/ 1 im) (/ 1 re)) in re * [misc]backup-simplify: Simplify (hypot (/ 1 im) (/ 1 re)) into (hypot (/ 1 im) (/ 1 re)) * [misc]backup-simplify: Simplify (log (hypot (/ 1 im) (/ 1 re))) into (log (hypot (/ 1 im) (/ 1 re))) * [misc]taylor: Taking taylor expansion of (log (hypot (/ 1 im) (/ 1 re))) in im * [misc]taylor: Taking taylor expansion of (hypot (/ 1 im) (/ 1 re)) in im * [misc]backup-simplify: Simplify (hypot (/ 1 im) (/ 1 re)) into (hypot (/ 1 im) (/ 1 re)) * [misc]backup-simplify: Simplify (log (hypot (/ 1 im) (/ 1 re))) into (log (hypot (/ 1 im) (/ 1 re))) * [misc]taylor: Taking taylor expansion of (log (hypot (/ 1 im) (/ 1 re))) in im * [misc]taylor: Taking taylor expansion of (hypot (/ 1 im) (/ 1 re)) in im * [misc]backup-simplify: Simplify (hypot (/ 1 im) (/ 1 re)) into (hypot (/ 1 im) (/ 1 re)) * [misc]backup-simplify: Simplify (log (hypot (/ 1 im) (/ 1 re))) into (log (hypot (/ 1 im) (/ 1 re))) * [misc]taylor: Taking taylor expansion of (log (hypot (/ 1 im) (/ 1 re))) in re * [misc]taylor: Taking taylor expansion of (hypot (/ 1 im) (/ 1 re)) in re * [misc]backup-simplify: Simplify (hypot (/ 1 im) (/ 1 re)) into (hypot (/ 1 im) (/ 1 re)) * [misc]backup-simplify: Simplify (log (hypot (/ 1 im) (/ 1 re))) into (log (hypot (/ 1 im) (/ 1 re))) * [misc]backup-simplify: Simplify (log (hypot (/ 1 im) (/ 1 re))) into (log (hypot (/ 1 im) (/ 1 re))) * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (hypot (/ 1 im) (/ 1 re)) 1)))) 1) into 0 * [misc]taylor: Taking taylor expansion of 0 in re * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (hypot (/ 1 im) (/ 1 re)) 1)))) 1) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (hypot (/ 1 im) (/ 1 re)) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (hypot (/ 1 im) (/ 1 re)) 1)))) 2) into 0 * [misc]taylor: Taking taylor expansion of 0 in re * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (hypot (/ 1 im) (/ 1 re)) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (hypot (/ 1 im) (/ 1 re)) 1)))) 2) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (hypot (/ 1 im) (/ 1 re)) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (hypot (/ 1 im) (/ 1 re)) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (hypot (/ 1 im) (/ 1 re)) 1)))) 6) into 0 * [misc]taylor: Taking taylor expansion of 0 in re * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (log (hypot (/ 1 im) (/ 1 re))) into (log (hypot (/ 1 im) (/ 1 re))) * [misc]approximate: Taking taylor expansion of (log (hypot (/ 1 (- im)) (/ 1 (- re)))) in (im re) around 0 * [misc]taylor: Taking taylor expansion of (log (hypot (/ 1 (- im)) (/ 1 (- re)))) in re * [misc]taylor: Taking taylor expansion of (hypot (/ 1 (- im)) (/ 1 (- re))) in re * [misc]backup-simplify: Simplify (hypot (/ 1 (- im)) (/ 1 (- re))) into (hypot (/ -1 im) (/ -1 re)) * [misc]backup-simplify: Simplify (log (hypot (/ -1 im) (/ -1 re))) into (log (hypot (/ -1 im) (/ -1 re))) * [misc]taylor: Taking taylor expansion of (log (hypot (/ 1 (- im)) (/ 1 (- re)))) in im * [misc]taylor: Taking taylor expansion of (hypot (/ 1 (- im)) (/ 1 (- re))) in im * [misc]backup-simplify: Simplify (hypot (/ 1 (- im)) (/ 1 (- re))) into (hypot (/ -1 im) (/ -1 re)) * [misc]backup-simplify: Simplify (log (hypot (/ -1 im) (/ -1 re))) into (log (hypot (/ -1 im) (/ -1 re))) * [misc]taylor: Taking taylor expansion of (log (hypot (/ 1 (- im)) (/ 1 (- re)))) in im * [misc]taylor: Taking taylor expansion of (hypot (/ 1 (- im)) (/ 1 (- re))) in im * [misc]backup-simplify: Simplify (hypot (/ 1 (- im)) (/ 1 (- re))) into (hypot (/ -1 im) (/ -1 re)) * [misc]backup-simplify: Simplify (log (hypot (/ -1 im) (/ -1 re))) into (log (hypot (/ -1 im) (/ -1 re))) * [misc]taylor: Taking taylor expansion of (log (hypot (/ -1 im) (/ -1 re))) in re * [misc]taylor: Taking taylor expansion of (hypot (/ -1 im) (/ -1 re)) in re * [misc]backup-simplify: Simplify (hypot (/ -1 im) (/ -1 re)) into (hypot (/ -1 im) (/ -1 re)) * [misc]backup-simplify: Simplify (log (hypot (/ -1 im) (/ -1 re))) into (log (hypot (/ -1 im) (/ -1 re))) * [misc]backup-simplify: Simplify (log (hypot (/ -1 im) (/ -1 re))) into (log (hypot (/ -1 im) (/ -1 re))) * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (hypot (/ -1 im) (/ -1 re)) 1)))) 1) into 0 * [misc]taylor: Taking taylor expansion of 0 in re * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (hypot (/ -1 im) (/ -1 re)) 1)))) 1) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (hypot (/ -1 im) (/ -1 re)) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (hypot (/ -1 im) (/ -1 re)) 1)))) 2) into 0 * [misc]taylor: Taking taylor expansion of 0 in re * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (hypot (/ -1 im) (/ -1 re)) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (hypot (/ -1 im) (/ -1 re)) 1)))) 2) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (hypot (/ -1 im) (/ -1 re)) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (hypot (/ -1 im) (/ -1 re)) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (hypot (/ -1 im) (/ -1 re)) 1)))) 6) into 0 * [misc]taylor: Taking taylor expansion of 0 in re * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (log (hypot (/ -1 im) (/ -1 re))) into (log (hypot (/ -1 im) (/ -1 re))) * * * [misc]progress: generating rewritten candidates * * * * [misc]progress: [ 1 / 1 ] rewriting at (2) * * * [misc]progress: simplifying candidates * * * * [misc]progress: [ 1 / 14 ] simplifiying candidate # * [enter]simplify: Simplifying (log (hypot im re)) * * [misc]simplify: iters left: 2 (4 enodes) * [exit]simplify: Simplified to (log (hypot im re)) * * * * [misc]progress: [ 2 / 14 ] simplifiying candidate # * [enter]simplify: Simplifying (log (hypot (/ 1 im) (/ 1 re))) * * [misc]simplify: iters left: 4 (7 enodes) * * [misc]simplify: iters left: 3 (9 enodes) * [exit]simplify: Simplified to (log (hypot (/ 1 im) (/ 1 re))) * * * * [misc]progress: [ 3 / 14 ] simplifiying candidate # * [enter]simplify: Simplifying (log (hypot (/ -1 im) (/ -1 re))) * * [misc]simplify: iters left: 4 (7 enodes) * [exit]simplify: Simplified to (log (hypot (/ -1 im) (/ -1 re))) * * * * [misc]progress: [ 4 / 14 ] simplifiying candidate # * [enter]simplify: Simplifying (expm1 (log (hypot im re))) * * [misc]simplify: iters left: 3 (5 enodes) * [exit]simplify: Simplified to (expm1 (log (hypot im re))) * [exit]simplify: Simplified to (expm1 (log (hypot im re))) * * * * [misc]progress: [ 5 / 14 ] simplifiying candidate # * [enter]simplify: Simplifying (log1p (log (hypot im re))) * * [misc]simplify: iters left: 3 (5 enodes) * [exit]simplify: Simplified to (log1p (log (hypot im re))) * [exit]simplify: Simplified to (log1p (log (hypot im re))) * * * * [misc]progress: [ 6 / 14 ] simplifiying candidate # * [enter]simplify: Simplifying (log 1) * * [misc]simplify: iters left: 1 (2 enodes) * [exit]simplify: Simplified to (log 1) * [exit]simplify: Simplified to (log 1) * [enter]simplify: Simplifying (log (hypot im re)) * * [misc]simplify: iters left: 2 (4 enodes) * [exit]simplify: Simplified to (log (hypot im re)) * [exit]simplify: Simplified to (log (hypot im re)) * * * * [misc]progress: [ 7 / 14 ] simplifiying candidate # * [enter]simplify: Simplifying (log (hypot im re)) * * [misc]simplify: iters left: 2 (4 enodes) * [exit]simplify: Simplified to (log (hypot im re)) * [exit]simplify: Simplified to (log (hypot im re)) * * * * [misc]progress: [ 8 / 14 ] simplifiying candidate # * * * * [misc]progress: [ 9 / 14 ] simplifiying candidate # * [enter]simplify: Simplifying (log (log (hypot im re))) * * [misc]simplify: iters left: 3 (5 enodes) * [exit]simplify: Simplified to (log (log (hypot im re))) * [exit]simplify: Simplified to (log (log (hypot im re))) * * * * [misc]progress: [ 10 / 14 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (log (hypot im re))) * * [misc]simplify: iters left: 3 (5 enodes) * [exit]simplify: Simplified to (hypot im re) * [exit]simplify: Simplified to (hypot im re) * * * * [misc]progress: [ 11 / 14 ] simplifiying candidate # * [enter]simplify: Simplifying (cbrt (log (hypot im re))) * * [misc]simplify: iters left: 3 (5 enodes) * [exit]simplify: Simplified to (cbrt (log (hypot im re))) * [exit]simplify: Simplified to (cbrt (log (hypot im re))) * * * * [misc]progress: [ 12 / 14 ] simplifiying candidate # * [enter]simplify: Simplifying (cube (log (hypot im re))) * * [misc]simplify: iters left: 3 (5 enodes) * * [misc]simplify: iters left: 2 (7 enodes) * * [misc]simplify: iters left: 1 (9 enodes) * [exit]simplify: Simplified to (cube (log (hypot im re))) * [exit]simplify: Simplified to (cube (log (hypot im re))) * * * * [misc]progress: [ 13 / 14 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (log (hypot im re))) * * [misc]simplify: iters left: 3 (5 enodes) * [exit]simplify: Simplified to (sqrt (log (hypot im re))) * [exit]simplify: Simplified to (sqrt (log (hypot im re))) * * * * [misc]progress: [ 14 / 14 ] simplifiying candidate # * * * [misc]progress: adding candidates to table * [misc]progress: [Phase 3 of 3] Extracting. * [enter]simplify: Simplifying (hypot im re) * * [misc]simplify: iters left: 1 (3 enodes) * [exit]simplify: Simplified to (hypot im re) * [exit]simplify: Simplified to (hypot im re)