Details

Time bar (total: 1.2m)

sample559.0ms

Algorithm
intervals
Results
331.0ms112×body1280valid
111.0ms73×body640valid
37.0ms256×pre80true
18.0ms17×body320valid
15.0ms48×body80valid
4.0ms6×body160valid

simplify89.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
88.0ms
(+ x (- (tan (+ y z)) (tan a)))

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.5b

localize37.0ms

Local error

Found 3 expressions with local error:

3.9b
(tan (+ y z))
0.2b
(- (tan (+ y z)) (tan a))
0.1b
(+ x (- (tan (+ y z)) (tan a)))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
24×*-un-lft-identity
19×add-sqr-sqrt
18×prod-diff
17×add-cube-cbrt
11×associate-+r+
10×add-log-exp
4×tan-quot
3×expm1-log1p-u pow1 fma-def add-cbrt-cube fma-neg add-exp-log insert-posit16 log1p-expm1-u
2×tan-sum sum-log sub-neg diff-log frac-sub distribute-lft-out distribute-lft-out--
1×+-commutative associate-+r- flip3-+ flip3-- flip-+ flip-- difference-of-squares
Counts
3 → 75
Calls
3 calls:
Slowest
30.0ms
(- (tan (+ y z)) (tan a))
25.0ms
(+ x (- (tan (+ y z)) (tan a)))
12.0ms
(tan (+ y z))

series441.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
188.0ms
(+ x (- (tan (+ y z)) (tan a)))
167.0ms
(- (tan (+ y z)) (tan a))
86.0ms
(tan (+ y z))

simplify3.6s

Counts
56 → 84
Calls
56 calls:
Slowest
272.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
197.0ms
(+ (* 1/3 (pow y 3)) (+ z y))
195.0ms
(fma (* (cbrt (tan (+ y z))) (cbrt (tan (+ y z)))) (cbrt (tan (+ y z))) (- (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a))))))
186.0ms
(fma (sqrt (tan (+ y z))) (sqrt (tan (+ y z))) (- (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a))))))
157.0ms
(fma (- (cbrt (tan a))) (* (cbrt (tan a)) (cbrt (tan a))) (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a)))))

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize49.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (tan y) (tan z))
0.2b
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
0.1b
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
0.1b
(+ (tan y) (tan z))

rewrite344.0ms

Algorithm
rewrite-expression-head
Rules
151×*-un-lft-identity
108×prod-diff
107×add-sqr-sqrt
100×add-cube-cbrt
85×times-frac
56×associate-+r+
24×distribute-lft-out
18×fma-neg
14×associate-/r/
13×add-log-exp
8×flip3-- flip--
7×tan-quot div-inv
6×pow1 fma-def add-cbrt-cube add-exp-log
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×sum-log associate-*r* associate-*l*
2×+-commutative sub-neg flip3-+ diff-log flip-+ distribute-lft-out-- difference-of-squares
1×frac-times associate-+r- pow-prod-down associate-*l/ frac-add prod-exp associate-*r/ *-commutative frac-sub cbrt-unprod unswap-sqr
Counts
4 → 211
Calls
4 calls:
Slowest
167.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
134.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
17.0ms
(* (tan y) (tan z))
17.0ms
(+ (tan y) (tan z))

series1.5s

Counts
4 → 12
Calls
4 calls:
Slowest
641.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
581.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
165.0ms
(* (tan y) (tan z))
136.0ms
(+ (tan y) (tan z))

simplify27.4s

Counts
228 → 223
Calls
228 calls:
Slowest
620.0ms
(fma (/ 1 (* (cbrt (- 1 (* (tan y) (tan z)))) (cbrt (- 1 (* (tan y) (tan z)))))) (/ (+ (tan y) (tan z)) (cbrt (- 1 (* (tan y) (tan z))))) (- (* (sqrt (tan a)) (sqrt (tan a)))))
593.0ms
(fma (/ (+ (tan y) (tan z)) (- (* 1 1) (* (* (tan y) (tan z)) (* (tan y) (tan z))))) (+ 1 (* (tan y) (tan z))) (- (* (tan a) 1)))
576.0ms
(fma (- (cbrt (tan a))) (* (cbrt (tan a)) (cbrt (tan a))) (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a)))))
543.0ms
(fma (/ 1 (* (cbrt (- 1 (* (tan y) (tan z)))) (cbrt (- 1 (* (tan y) (tan z)))))) (/ (+ (tan y) (tan z)) (cbrt (- 1 (* (tan y) (tan z))))) (- (* (sqrt (tan a)) (sqrt (tan a)))))
482.0ms
(fma (/ (+ (tan y) (tan z)) (- (* 1 1) (* (* (tan y) (tan z)) (* (tan y) (tan z))))) (+ 1 (* (tan y) (tan z))) (- (* (sqrt (tan a)) (sqrt (tan a)))))

prune4.0s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (tan y) (tan z))
0.2b
(fma (+ (tan y) (tan z)) (/ 1 (- 1 (* (tan y) (tan z)))) (- (tan a)))
0.2b
(+ x (fma (+ (tan y) (tan z)) (/ 1 (- 1 (* (tan y) (tan z)))) (- (tan a))))
0.1b
(+ (tan y) (tan z))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
12×*-un-lft-identity
10×add-sqr-sqrt
8×add-cube-cbrt add-log-exp
6×pow1 fma-def add-cbrt-cube tan-quot add-exp-log
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-*r* associate-*l*
2×+-commutative sum-log flip3-+ flip-+ fma-udef distribute-lft-out
1×frac-times associate-+r+ pow-prod-down associate-*l/ frac-add prod-exp associate-*r/ *-commutative cbrt-unprod unswap-sqr
Counts
4 → 73
Calls
4 calls:
Slowest
19.0ms
(* (tan y) (tan z))
17.0ms
(+ (tan y) (tan z))
10.0ms
(+ x (fma (+ (tan y) (tan z)) (/ 1 (- 1 (* (tan y) (tan z)))) (- (tan a))))
1.0ms
(fma (+ (tan y) (tan z)) (/ 1 (- 1 (* (tan y) (tan z)))) (- (tan a)))

series1.4s

Counts
4 → 12
Calls
4 calls:
Slowest
551.0ms
(fma (+ (tan y) (tan z)) (/ 1 (- 1 (* (tan y) (tan z)))) (- (tan a)))
523.0ms
(+ x (fma (+ (tan y) (tan z)) (/ 1 (- 1 (* (tan y) (tan z)))) (- (tan a))))
157.0ms
(* (tan y) (tan z))
152.0ms
(+ (tan y) (tan z))

simplify3.4s

Counts
37 → 85
Calls
37 calls:
Slowest
408.0ms
(* (* (* (tan y) (tan y)) (tan y)) (* (* (tan z) (tan z)) (tan z)))
407.0ms
(- (+ (/ (sin z) (* (cos z) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z)))))) (+ (/ (sin y) (* (cos y) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z)))))) x)) (/ (sin a) (cos a)))
397.0ms
(- (+ (/ (sin z) (* (cos z) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z)))))) (+ (/ (sin y) (* (cos y) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z)))))) x)) (/ (sin a) (cos a)))
366.0ms
(+ x (fma (+ (tan y) (tan z)) (/ 1 (- 1 (* (tan y) (tan z)))) (- (tan a))))
333.0ms
(+ (* 1/3 (* (pow z 3) y)) (+ (* 1/3 (* z (pow y 3))) (* z y)))

prune1.7s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize88.0ms

Local error

Found 4 expressions with local error:

0.2b
(fma (+ (tan y) (tan z)) (/ 1 (- 1 (/ (* (tan y) (sin z)) (cos z)))) (- (tan a)))
0.2b
(* (tan y) (sin z))
0.2b
(+ x (fma (+ (tan y) (tan z)) (/ 1 (- 1 (/ (* (tan y) (sin z)) (cos z)))) (- (tan a))))
0.2b
(/ (* (tan y) (sin z)) (cos z))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity add-cbrt-cube add-exp-log
9×add-cube-cbrt
6×pow1 add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-/r* fma-def times-frac associate-*r* associate-*l*
2×cbrt-undiv div-exp associate-*l/ prod-exp tan-quot cbrt-unprod fma-udef
1×+-commutative associate-+r+ clear-num sum-log frac-2neg flip3-+ pow-prod-down *-commutative flip-+ div-inv distribute-lft-out associate-/l* unswap-sqr associate-/l/
Counts
4 → 77
Calls
4 calls:
Slowest
32.0ms
(/ (* (tan y) (sin z)) (cos z))
29.0ms
(* (tan y) (sin z))
9.0ms
(+ x (fma (+ (tan y) (tan z)) (/ 1 (- 1 (/ (* (tan y) (sin z)) (cos z)))) (- (tan a))))
1.0ms
(fma (+ (tan y) (tan z)) (/ 1 (- 1 (/ (* (tan y) (sin z)) (cos z)))) (- (tan a)))

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
537.0ms
(fma (+ (tan y) (tan z)) (/ 1 (- 1 (/ (* (tan y) (sin z)) (cos z)))) (- (tan a)))
463.0ms
(+ x (fma (+ (tan y) (tan z)) (/ 1 (- 1 (/ (* (tan y) (sin z)) (cos z)))) (- (tan a))))
193.0ms
(/ (* (tan y) (sin z)) (cos z))
109.0ms
(* (tan y) (sin z))

simplify4.1s

Counts
43 → 89
Calls
43 calls:
Slowest
434.0ms
(- (+ (/ (sin z) (* (cos z) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z)))))) (+ (/ (sin y) (* (cos y) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z)))))) x)) (/ (sin a) (cos a)))
427.0ms
(* (* (* (tan y) (tan y)) (tan y)) (* (* (sin z) (sin z)) (sin z)))
426.0ms
(- (+ (* 1/3 (* z (pow y 3))) (* z y)) (* 1/6 (* (pow z 3) y)))
392.0ms
(- (+ (/ (sin z) (* (cos z) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z)))))) (+ (/ (sin y) (* (cos y) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z)))))) x)) (/ (sin a) (cos a)))
320.0ms
(* (exp x) (exp (fma (+ (tan y) (tan z)) (/ 1 (- 1 (/ (* (tan y) (sin z)) (cos z)))) (- (tan a)))))

prune2.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes1.1s

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch4.0ms

end0.0ms

sample16.9s

Algorithm
intervals
Results
10.8s3844×body1280valid
3.2s2091×body640valid
1.1s8000×pre80true
679.0ms631×body320valid
377.0ms1153×body80valid
232.0ms281×body160valid