Details

Time bar (total: 56.1s)

sample66.0ms

Algorithm
intervals
Results
51.0ms304×body80valid

simplify512.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
512.0ms
(* (* (/ PI 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b)))

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.3b

localize35.0ms

Local error

Found 4 expressions with local error:

5.6b
(- (* b b) (* a a))
5.6b
(- (* b b) (* a a))
4.9b
(/ (/ PI (- (* b b) (* a a))) a)
3.9b
(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (/ (/ PI (- (* b b) (* a a))) a))

rewrite55.0ms

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/
Counts
4 → 140
Calls
4 calls:
Slowest
33.0ms
(/ (/ PI (- (* b b) (* a a))) a)
10.0ms
(- (* b b) (* a a))
9.0ms
(- (* b b) (* a a))
0.0ms
(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (/ (/ PI (- (* b b) (* a a))) a))

series291.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
96.0ms
(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (/ (/ PI (- (* b b) (* a a))) a))
95.0ms
(/ (/ PI (- (* b b) (* a a))) a)
54.0ms
(- (* b b) (* a a))
46.0ms
(- (* b b) (* a a))

simplify20.7s

Counts
152 → 152
Calls
152 calls:
Slowest
571.0ms
(/ (/ PI (- (* b b) (* a a))) a)
555.0ms
(/ (/ PI (- (* (* b b) (* b b)) (* (* a a) (* a a)))) 1)
490.0ms
(/ (/ PI (- (pow (* b b) 3) (pow (* a a) 3))) (* (cbrt a) (cbrt a)))
398.0ms
(/ (/ PI (- (pow (* b b) 3) (pow (* a a) 3))) (sqrt a))
350.0ms
(- (log (/ PI (- (* b b) (* a a)))) (log a))

prune1.8s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 4.3b

localize38.0ms

Local error

Found 4 expressions with local error:

5.6b
(- (* b b) (* a a))
3.9b
(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (/ (/ 1 (+ b a)) (/ a (/ PI (- b a)))))
1.2b
(/ PI (- (* b b) (* a a)))
0.3b
(/ PI (- b a))

rewrite34.0ms

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
Counts
4 → 105
Calls
4 calls:
Slowest
13.0ms
(- (* b b) (* a a))
11.0ms
(/ PI (- (* b b) (* a a)))
8.0ms
(/ PI (- b a))
0.0ms
(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (/ (/ 1 (+ b a)) (/ a (/ PI (- b a)))))

series279.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
127.0ms
(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (/ (/ 1 (+ b a)) (/ a (/ PI (- b a)))))
56.0ms
(- (* b b) (* a a))
48.0ms
(/ PI (- (* b b) (* a a)))
47.0ms
(/ PI (- b a))

simplify4.4s

Counts
92 → 117
Calls
92 calls:
Slowest
314.0ms
(+ (* (* b b) (* b b)) (+ (* (* a a) (* a a)) (* (* b b) (* a a))))
200.0ms
(/ (* (cbrt PI) (cbrt PI)) (* (cbrt (- (* b b) (* a a))) (cbrt (- (* b b) (* a a)))))
194.0ms
(- (log PI) (log (- (* b b) (* a a))))
178.0ms
(/ (* (* PI PI) PI) (* (* (- b a) (- b a)) (- b a)))
178.0ms
(/ (exp (* b b)) (exp (* a a)))

prune1.6s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.8b

localize66.0ms

Local error

Found 4 expressions with local error:

3.9b
(fma (/ (/ PI (+ b a)) (- b a)) (/ -1 b) (/ (/ 1 (+ b a)) (/ a (/ PI (- b a)))))
0.3b
(/ PI (- b a))
0.2b
(/ PI (+ b a))
0.2b
(/ a (/ PI (- b a)))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
150×times-frac
121×*-un-lft-identity
113×add-sqr-sqrt
81×add-cube-cbrt
30×associate-/r*
16×distribute-lft-out-- difference-of-squares
13×add-cbrt-cube add-exp-log associate-/r/
9×associate-/l*
7×div-inv
5×cbrt-undiv flip3-- div-exp flip--
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u distribute-lft-out add-log-exp
3×clear-num frac-2neg
1×flip3-+ flip-+ fma-udef
Counts
4 → 192
Calls
4 calls:
Slowest
20.0ms
(/ a (/ PI (- b a)))
16.0ms
(/ PI (- b a))
15.0ms
(/ PI (+ b a))
1.0ms
(fma (/ (/ PI (+ b a)) (- b a)) (/ -1 b) (/ (/ 1 (+ b a)) (/ a (/ PI (- b a)))))

series376.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
140.0ms
(fma (/ (/ PI (+ b a)) (- b a)) (/ -1 b) (/ (/ 1 (+ b a)) (/ a (/ PI (- b a)))))
99.0ms
(/ a (/ PI (- b a)))
69.0ms
(/ PI (+ b a))
69.0ms
(/ PI (- b a))

simplify12.6s

Counts
241 → 204
Calls
241 calls:
Slowest
588.0ms
(/ (* (* a a) a) (* (* (/ PI (- b a)) (/ PI (- b a))) (/ PI (- b a))))
476.0ms
(/ (* (cbrt a) (cbrt a)) (/ (* (cbrt PI) (cbrt PI)) (* (cbrt (- b a)) (cbrt (- b a)))))
457.0ms
(/ 1 (/ PI (- (* b b) (* a a))))
387.0ms
(/ (sqrt a) (/ PI (- (* b b) (* a a))))
367.0ms
(/ (* (* PI PI) PI) (* (* (+ b a) (+ b a)) (+ b a)))

prune2.5s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 3.8b

localize53.0ms

Local error

Found 4 expressions with local error:

3.9b
(fma (/ (/ PI (+ b a)) (- b a)) (/ -1 b) (/ (/ 1 (+ b a)) (* (/ a PI) (- b a))))
0.2b
(/ a PI)
0.2b
(/ PI (+ b a))
0.2b
(* (/ a PI) (- b a))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
51×*-un-lft-identity
48×add-sqr-sqrt
41×add-cube-cbrt
31×times-frac
18×prod-diff
13×add-cbrt-cube associate-*l* add-exp-log
11×distribute-rgt-in distribute-lft-in
7×associate-/r*
6×pow1 associate-/l*
5×associate-*r*
4×expm1-log1p-u insert-posit16 log1p-expm1-u distribute-lft-out add-log-exp
3×cbrt-undiv div-exp div-inv
2×frac-times clear-num sub-neg frac-2neg flip3-- prod-exp associate-*r/ associate-/r/ cbrt-unprod flip-- unswap-sqr
1×flip3-+ pow-prod-down associate-*l/ *-commutative flip-+ fma-udef distribute-lft-out-- difference-of-squares
Counts
4 → 140
Calls
4 calls:
Slowest
24.0ms
(* (/ a PI) (- b a))
12.0ms
(/ PI (+ b a))
8.0ms
(/ a PI)
1.0ms
(fma (/ (/ PI (+ b a)) (- b a)) (/ -1 b) (/ (/ 1 (+ b a)) (* (/ a PI) (- b a))))

series355.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
143.0ms
(fma (/ (/ PI (+ b a)) (- b a)) (/ -1 b) (/ (/ 1 (+ b a)) (* (/ a PI) (- b a))))
104.0ms
(* (/ a PI) (- b a))
66.0ms
(/ PI (+ b a))
42.0ms
(/ a PI)

simplify5.8s

Counts
124 → 152
Calls
124 calls:
Slowest
425.0ms
(* a (- (* b b) (* a a)))
413.0ms
(/ (* (* a a) a) (* (* PI PI) PI))
388.0ms
(* a (- (pow b 3) (pow a 3)))
332.0ms
(/ (* (* PI PI) PI) (* (* (+ b a) (+ b a)) (+ b a)))
256.0ms
(* (/ a PI) (fma (- (cbrt a)) (* (cbrt a) (cbrt a)) (* (cbrt a) (* (cbrt a) (cbrt a)))))

prune2.3s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.8b

regimes240.0ms

Accuracy

0% (0.2b remaining)

Error of 4.4b against oracle of 4.2b and baseline of 4.4b

bsearch4.0ms

end0.0ms

sample2.0s

Algorithm
intervals
Results
1.8s9626×body80valid