Details

Time bar (total: 2.5m)

sample499.0ms

Algorithm
intervals
Results
123.0ms52×body1280valid
89.0ms149×body80valid
84.0ms49×body640valid
21.0ms61×body80nan
17.0ms15×body320valid
13.0ms17×body160valid

simplify432.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
431.0ms
(+ (- (* x (/ 1 (tan B)))) (* (/ F (sin B)) (pow (+ (+ (* F F) 2) (* 2 x)) (- (/ 1 2)))))

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.3b

localize46.0ms

Local error

Found 4 expressions with local error:

14.9b
(pow (fma 2 x (fma F F 2)) -1/2)
5.4b
(/ (pow (fma 2 x (fma F F 2)) -1/2) (/ (sin B) F))
0.2b
(/ x (tan B))
0.1b
(/ (sin B) F)

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
181×times-frac
106×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
45×unpow-prod-down
22×add-exp-log
19×associate-/r*
15×sqr-pow
13×add-cbrt-cube associate-/l*
11×div-exp div-inv
5×pow1 cbrt-undiv
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×pow-to-exp pow-unpow clear-num frac-2neg pow-exp
2×associate-/r/
1×pow-pow tan-quot
Counts
4 → 214
Calls
4 calls:
Slowest
13.0ms
(/ (sin B) F)
8.0ms
(/ (pow (fma 2 x (fma F F 2)) -1/2) (/ (sin B) F))
5.0ms
(/ x (tan B))
3.0ms
(pow (fma 2 x (fma F F 2)) -1/2)

series656.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
262.0ms
(pow (fma 2 x (fma F F 2)) -1/2)
222.0ms
(/ (pow (fma 2 x (fma F F 2)) -1/2) (/ (sin B) F))
126.0ms
(/ x (tan B))
46.0ms
(/ (sin B) F)

simplify53.9s

Counts
278 → 226
Calls
278 calls:
Slowest
768.0ms
(/ (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (sin B))
710.0ms
(/ (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (/ 1 (* (cbrt F) (cbrt F))))
616.0ms
(/ (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (/ (* (cbrt (sin B)) (cbrt (sin B))) (sqrt F)))
610.0ms
(/ (pow (* (cbrt (fma 2 x (fma F F 2))) (cbrt (fma 2 x (fma F F 2)))) -1/2) (/ 1 (* (cbrt F) (cbrt F))))
574.0ms
(- (+ (* 3/2 (/ (* (sqrt 1/32) (* (pow x 2) F)) B)) (/ (* F (sqrt 1/2)) B)) (/ (* x (* F (sqrt 1/8))) B))

prune3.5s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 9.0b

localize50.0ms

Local error

Found 4 expressions with local error:

14.9b
(pow (fma 2 x (fma F F 2)) -1/2)
0.4b
(/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B))
0.3b
(* (/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B)) F)
0.2b
(/ x (tan B))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
55×add-sqr-sqrt
54×times-frac
45×*-un-lft-identity add-cube-cbrt
25×unpow-prod-down associate-*l*
22×add-exp-log
13×add-cbrt-cube
10×associate-/l*
9×sqr-pow
7×pow1 div-exp
6×associate-/r*
4×expm1-log1p-u prod-exp insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×pow-to-exp cbrt-undiv pow-unpow associate-*r* pow-exp div-inv
2×clear-num frac-2neg cbrt-unprod
1×pow-pow pow-prod-down associate-*l/ tan-quot associate-/r/ *-commutative
Counts
4 → 150
Calls
4 calls:
Slowest
13.0ms
(* (/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B)) F)
7.0ms
(/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B))
6.0ms
(/ x (tan B))
2.0ms
(pow (fma 2 x (fma F F 2)) -1/2)

series872.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
287.0ms
(pow (fma 2 x (fma F F 2)) -1/2)
222.0ms
(* (/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B)) F)
201.0ms
(/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B))
161.0ms
(/ x (tan B))

simplify23.3s

Counts
142 → 162
Calls
142 calls:
Slowest
850.0ms
(/ (* (* (pow (fma 2 x (fma F F 2)) -1/2) (pow (fma 2 x (fma F F 2)) -1/2)) (pow (fma 2 x (fma F F 2)) -1/2)) (* (* (sin B) (sin B)) (sin B)))
818.0ms
(* (* (* (/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B)) (/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B))) (/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B))) (* (* F F) F))
527.0ms
(- (+ (pow 2 -1/2) (* 3/2 (* (sqrt 1/32) (pow x 2)))) (* x (sqrt 1/8)))
493.0ms
(/ (pow (* (cbrt (fma 2 x (fma F F 2))) (cbrt (fma 2 x (fma F F 2)))) -1/2) 1)
477.0ms
(/ (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (sqrt (sin B)))

prune2.9s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 9.0b

localize39.0ms

Local error

Found 4 expressions with local error:

14.9b
(pow (fma 2 x (fma F F 2)) -1/2)
0.4b
(/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B))
0.3b
(* (/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B)) F)
0.2b
(* (/ x (sin B)) (cos B))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
60×add-sqr-sqrt
55×times-frac
45×*-un-lft-identity add-cube-cbrt
38×associate-*l*
25×unpow-prod-down add-exp-log
16×add-cbrt-cube
9×pow1 sqr-pow
7×div-exp associate-/l*
6×associate-*r* prod-exp unswap-sqr
4×expm1-log1p-u cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×pow-to-exp cbrt-undiv pow-unpow associate-/r* pow-exp div-inv
2×pow-prod-down associate-*l/ *-commutative
1×clear-num pow-pow frac-2neg
Counts
4 → 154
Calls
4 calls:
Slowest
18.0ms
(* (/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B)) F)
14.0ms
(* (/ x (sin B)) (cos B))
12.0ms
(/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B))
4.0ms
(pow (fma 2 x (fma F F 2)) -1/2)

series771.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
260.0ms
(pow (fma 2 x (fma F F 2)) -1/2)
215.0ms
(* (/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B)) F)
167.0ms
(/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B))
129.0ms
(* (/ x (sin B)) (cos B))

simplify24.3s

Counts
140 → 166
Calls
140 calls:
Slowest
808.0ms
(/ (* (* (pow (fma 2 x (fma F F 2)) -1/2) (pow (fma 2 x (fma F F 2)) -1/2)) (pow (fma 2 x (fma F F 2)) -1/2)) (* (* (sin B) (sin B)) (sin B)))
774.0ms
(* (* (* (/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B)) (/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B))) (/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B))) (* (* F F) F))
588.0ms
(/ (pow (* (cbrt (fma 2 x (fma F F 2))) (cbrt (fma 2 x (fma F F 2)))) -1/2) 1)
586.0ms
(- (+ (pow 2 -1/2) (* 3/2 (* (sqrt 1/32) (pow x 2)))) (* x (sqrt 1/8)))
509.0ms
(/ (pow (* (cbrt (fma 2 x (fma F F 2))) (cbrt (fma 2 x (fma F F 2)))) -1/2) 1)

prune3.0s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 9.0b

localize57.0ms

Local error

Found 4 expressions with local error:

15.4b
(pow (fma 2 x (fma F F 2)) (/ -1/2 2))
15.4b
(pow (fma 2 x (fma F F 2)) (/ -1/2 2))
0.7b
(* (pow (fma 2 x (fma F F 2)) (/ -1/2 2)) (pow (fma 2 x (fma F F 2)) (/ -1/2 2)))
0.4b
(/ (* (pow (fma 2 x (fma F F 2)) (/ -1/2 2)) (pow (fma 2 x (fma F F 2)) (/ -1/2 2))) (sin B))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
42×add-sqr-sqrt
41×add-exp-log
30×*-un-lft-identity add-cube-cbrt
26×pow-unpow
24×unpow-prod-down
21×times-frac
18×prod-exp
14×pow-to-exp pow-exp
12×sqr-pow
11×add-cbrt-cube
10×div-exp
9×unswap-sqr
7×swap-sqr associate-*r* associate-*l*
6×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* div-inv
2×cbrt-undiv pow-pow cbrt-unprod
1×pow2 clear-num frac-2neg pow-prod-down pow-sqr *-commutative pow-prod-up associate-/l*
Counts
4 → 147
Calls
4 calls:
Slowest
26.0ms
(* (pow (fma 2 x (fma F F 2)) (/ -1/2 2)) (pow (fma 2 x (fma F F 2)) (/ -1/2 2)))
23.0ms
(/ (* (pow (fma 2 x (fma F F 2)) (/ -1/2 2)) (pow (fma 2 x (fma F F 2)) (/ -1/2 2))) (sin B))
3.0ms
(pow (fma 2 x (fma F F 2)) (/ -1/2 2))
3.0ms
(pow (fma 2 x (fma F F 2)) (/ -1/2 2))

series865.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
291.0ms
(pow (fma 2 x (fma F F 2)) (/ -1/2 2))
275.0ms
(pow (fma 2 x (fma F F 2)) (/ -1/2 2))
194.0ms
(/ (* (pow (fma 2 x (fma F F 2)) (/ -1/2 2)) (pow (fma 2 x (fma F F 2)) (/ -1/2 2))) (sin B))
105.0ms
(* (pow (fma 2 x (fma F F 2)) (/ -1/2 2)) (pow (fma 2 x (fma F F 2)) (/ -1/2 2)))

simplify18.7s

Counts
131 → 159
Calls
131 calls:
Slowest
518.0ms
(+ (log (pow (fma 2 x (fma F F 2)) (/ -1/2 2))) (* (log (fma 2 x (fma F F 2))) (/ -1/2 2)))
470.0ms
(+ (log (pow (fma 2 x (fma F F 2)) (/ -1/2 2))) (* (log (fma 2 x (fma F F 2))) (/ -1/2 2)))
437.0ms
(- (+ (* 5/8 (* (pow x 2) (pow 1/512 1/4))) (pow 2 -1/4)) (* 1/2 (* x (pow 1/32 1/4))))
432.0ms
(* (* (cbrt (pow (fma 2 x (fma F F 2)) (/ -1/2 2))) (cbrt (pow (fma 2 x (fma F F 2)) (/ -1/2 2)))) (* (cbrt (pow (fma 2 x (fma F F 2)) (/ -1/2 2))) (cbrt (pow (fma 2 x (fma F F 2)) (/ -1/2 2)))))
425.0ms
(- (+ (* 5/8 (* (pow x 2) (pow 1/512 1/4))) (pow 2 -1/4)) (* 1/2 (* x (pow 1/32 1/4))))

prune2.5s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 9.0b

regimes409.0ms

Accuracy

0% (0.7b remaining)

Error of 10.7b against oracle of 10.0b and baseline of 10.7b

bsearch7.0ms

end0.0ms

sample14.1s

Algorithm
intervals
Results
5.8s1678×body1280valid
3.7s1427×body640valid
2.2s4739×body80valid
1.0s680×body320valid
735.0ms1664×body80nan
318.0ms331×body160valid