Details

Time bar (total: 55.1s)

sample61.0ms

Algorithm
intervals
Results
47.0ms319×body80valid

simplify428.0ms

Calls
1 calls:
Slowest
428.0ms
(* (* (/ PI 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b)))

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.9b

localize44.0ms

Local error

Found 4 expressions with local error:

5.5b
(- (* b b) (* a a))
5.5b
(- (* b b) (* a a))
5.1b
(/ (/ PI (- (* b b) (* a a))) a)
4.7b
(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (/ (/ PI (- (* b b) (* a a))) a))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
102×times-frac
55×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
18×associate-/l*
14×difference-of-squares
9×add-cbrt-cube add-exp-log
8×associate-/r/ add-log-exp
6×flip3-- flip--
5×div-inv
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u
3×cbrt-undiv associate-/r* div-exp
2×sub-neg fma-neg diff-log prod-diff
1×clear-num frac-2neg fma-udef associate-/l/
Calls
4 calls:
Slowest
24.0ms
(/ (/ PI (- (* b b) (* a a))) a)
18.0ms
(- (* b b) (* a a))
13.0ms
(- (* b b) (* a a))
0.0ms
(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (/ (/ PI (- (* b b) (* a a))) a))

series289.0ms

Calls
4 calls:
Slowest
117.0ms
(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (/ (/ PI (- (* b b) (* a a))) a))
74.0ms
(/ (/ PI (- (* b b) (* a a))) a)
53.0ms
(- (* b b) (* a a))
44.0ms
(- (* b b) (* a a))

simplify20.1s

Calls
152 calls:
Slowest
620.0ms
(/ (/ PI (- (* b b) (* a a))) (sqrt a))
507.0ms
(/ (/ PI (- (* (* b b) (* b b)) (* (* a a) (* a a)))) 1)
462.0ms
(/ (/ PI (- (pow (* b b) 3) (pow (* a a) 3))) (* (cbrt a) (cbrt a)))
396.0ms
(/ (/ PI (- (pow (* b b) 3) (pow (* a a) 3))) (sqrt a))
354.0ms
(/ (/ PI (- (pow (* b b) 3) (pow (* a a) 3))) 1)

prune1.8s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.3b

localize51.0ms

Local error

Found 4 expressions with local error:

5.5b
(- (* b b) (* a a))
4.7b
(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (/ (/ 1 (+ b a)) (/ a (/ PI (- b a)))))
0.9b
(/ PI (- (* b b) (* a a)))
0.2b
(/ PI (- b a))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
31×add-sqr-sqrt *-un-lft-identity
27×times-frac
23×add-cube-cbrt
9×associate-/r* difference-of-squares
8×add-cbrt-cube add-exp-log
6×associate-/l* add-log-exp
4×expm1-log1p-u pow1 associate-/r/ insert-posit16 log1p-expm1-u distribute-lft-out--
3×flip3-- flip--
2×cbrt-undiv clear-num frac-2neg div-exp div-inv
1×sub-neg fma-neg diff-log prod-diff fma-udef
Calls
4 calls:
Slowest
30.0ms
(/ PI (- (* b b) (* a a)))
16.0ms
(- (* b b) (* a a))
15.0ms
(/ PI (- b a))
0.0ms
(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (/ (/ 1 (+ b a)) (/ a (/ PI (- b a)))))

series274.0ms

Calls
4 calls:
Slowest
110.0ms
(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (/ (/ 1 (+ b a)) (/ a (/ PI (- b a)))))
71.0ms
(/ PI (- (* b b) (* a a)))
56.0ms
(/ PI (- b a))
37.0ms
(- (* b b) (* a a))

simplify4.1s

Calls
92 calls:
Slowest
263.0ms
(+ (* (* b b) (* b b)) (+ (* (* a a) (* a a)) (* (* b b) (* a a))))
228.0ms
(/ (exp (* b b)) (exp (* a a)))
170.0ms
(/ (* (* PI PI) PI) (* (* (- b a) (- b a)) (- b a)))
170.0ms
(/ (* (cbrt PI) (cbrt PI)) (sqrt (- (* b b) (* a a))))
168.0ms
(/ PI (sqrt (- (* b b) (* a a))))

prune1.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.7b

localize63.0ms

Local error

Found 4 expressions with local error:

4.7b
(fma (* (/ 1 (+ b a)) (/ PI (- b a))) (/ -1 b) (/ (/ 1 (+ b a)) (/ a (/ PI (- b a)))))
0.2b
(/ PI (- b a))
0.2b
(/ PI (- b a))
0.2b
(/ a (/ PI (- b a)))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
153×times-frac
122×add-sqr-sqrt *-un-lft-identity
82×add-cube-cbrt
31×associate-/r*
20×distribute-lft-out-- difference-of-squares
13×add-cbrt-cube add-exp-log associate-/r/
9×associate-/l*
7×div-inv
6×flip3-- flip--
5×cbrt-undiv div-exp
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg
1×fma-udef
Calls
4 calls:
Slowest
20.0ms
(/ a (/ PI (- b a)))
16.0ms
(/ PI (- b a))
15.0ms
(/ PI (- b a))
1.0ms
(fma (* (/ 1 (+ b a)) (/ PI (- b a))) (/ -1 b) (/ (/ 1 (+ b a)) (/ a (/ PI (- b a)))))

series366.0ms

Calls
4 calls:
Slowest
169.0ms
(fma (* (/ 1 (+ b a)) (/ PI (- b a))) (/ -1 b) (/ (/ 1 (+ b a)) (/ a (/ PI (- b a)))))
77.0ms
(/ a (/ PI (- b a)))
67.0ms
(/ PI (- b a))
52.0ms
(/ PI (- b a))

simplify12.7s

Calls
248 calls:
Slowest
608.0ms
(/ (* (* a a) a) (* (* (/ PI (- b a)) (/ PI (- b a))) (/ PI (- b a))))
484.0ms
(/ (* (cbrt a) (cbrt a)) (/ (* (cbrt PI) (cbrt PI)) (* (cbrt (- b a)) (cbrt (- b a)))))
475.0ms
(/ (sqrt a) (/ PI (- (* b b) (* a a))))
457.0ms
(/ 1 (/ PI (- (* b b) (* a a))))
325.0ms
(/ (* (cbrt a) (cbrt a)) (/ (* (cbrt PI) (cbrt PI)) (+ (sqrt b) (sqrt a))))

prune2.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.7b

localize33.0ms

Local error

Found 4 expressions with local error:

4.7b
(fma (* (/ 1 (+ b a)) (/ PI (- b a))) (/ -1 b) (/ (/ 1 (+ b a)) (* (/ a PI) (- b a))))
0.3b
(/ a PI)
0.2b
(/ PI (- b a))
0.2b
(* (/ a PI) (- b a))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
57×add-sqr-sqrt
52×*-un-lft-identity
42×add-cube-cbrt
34×times-frac
18×prod-diff
13×add-cbrt-cube associate-*l* add-exp-log
11×distribute-rgt-in distribute-lft-in
8×associate-/r*
6×pow1 associate-/l*
5×associate-*r* distribute-lft-out-- difference-of-squares
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv flip3-- div-exp div-inv flip--
2×frac-times clear-num sub-neg frac-2neg prod-exp associate-*r/ associate-/r/ cbrt-unprod unswap-sqr
1×pow-prod-down associate-*l/ *-commutative fma-udef
Calls
4 calls:
Slowest
46.0ms
(* (/ a PI) (- b a))
16.0ms
(/ PI (- b a))
8.0ms
(/ a PI)
0.0ms
(fma (* (/ 1 (+ b a)) (/ PI (- b a))) (/ -1 b) (/ (/ 1 (+ b a)) (* (/ a PI) (- b a))))

series688.0ms

Calls
4 calls:
Slowest
478.0ms
(fma (* (/ 1 (+ b a)) (/ PI (- b a))) (/ -1 b) (/ (/ 1 (+ b a)) (* (/ a PI) (- b a))))
85.0ms
(* (/ a PI) (- b a))
72.0ms
(/ PI (- b a))
52.0ms
(/ a PI)

simplify5.7s

Calls
131 calls:
Slowest
426.0ms
(* a (- (* b b) (* a a)))
420.0ms
(/ (* (* a a) a) (* (* PI PI) PI))
384.0ms
(* a (- (pow b 3) (pow a 3)))
210.0ms
(* (/ (* (* a a) a) (* (* PI PI) PI)) (* (* (- b a) (- b a)) (- b a)))
204.0ms
(* (/ a PI) (fma (- (cbrt a)) (* (cbrt a) (cbrt a)) (* (cbrt a) (* (cbrt a) (cbrt a)))))

prune1.9s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.7b

regimes187.0ms

Accuracy

0% (0.2b remaining)

Error of 4.7b against oracle of 4.5b and baseline of 4.7b

bsearch3.0ms

end0.0ms

sample2.0s

Algorithm
intervals
Results
1.8s9538×body80valid