Details

Time bar (total: 26.6s)

sample371.0ms

Algorithm
intervals
Results
125.0ms218×body10240exit
85.0ms235×body80valid
33.0ms395×body80nan
5.0ms23×body160valid

simplify1.5s

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
01012
11912
22812
34112
47612
518512
676412
done500012

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.1b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
0.0b
(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
4.4b
(- (exp (* 2.0 x)) 1.0)
4.4b
(- (exp x) 1.0)

rewrite220.0ms

Algorithm
rewrite-expression-head
Rules
92×add-sqr-sqrt
89×*-un-lft-identity
51×times-frac
41×add-cube-cbrt
31×sqrt-prod
24×distribute-lft-out-- difference-of-squares
18×prod-diff
8×add-log-exp
6×add-exp-log fma-neg add-cbrt-cube
5×pow1 flip3-- associate-/r* flip-- associate-/l*
4×expm1-log1p-u associate-/r/ log1p-expm1-u
2×sub-neg rem-sqrt-square diff-log div-inv associate-/l/
1×cbrt-undiv frac-2neg sqrt-pow1 pow1/2 sqrt-div div-sub div-exp clear-num
Counts
4 → 155
Calls
4 calls:
59.0ms
(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
91.0ms
(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
29.0ms
(- (exp (* 2.0 x)) 1.0)
26.0ms
(- (exp x) 1.0)

series369.0ms

Counts
4 → 12
Calls
4 calls:
164.0ms
(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
112.0ms
(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
44.0ms
(- (exp (* 2.0 x)) 1.0)
48.0ms
(- (exp x) 1.0)

simplify1.6s

Counts
167 → 167
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02322954
15032694
215322473
done50002423

prune1.1s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0))) (+ (exp x) 1.0)))
0.0b
(+ (exp x) 1.0)
4.4b
(- (exp (* 2.0 x)) 1.0)
4.4b
(- (exp (+ x x)) (* 1.0 1.0))

rewrite297.0ms

Algorithm
rewrite-expression-head
Rules
18×*-un-lft-identity
17×add-sqr-sqrt
14×add-cube-cbrt
13×prod-diff
10×add-log-exp
7×pow1 fma-neg
5×sqrt-div
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×fma-def flip3-+ exp-sum flip-+ difference-of-squares
2×frac-times sub-neg flip3-- sqrt-pow1 diff-log associate-*r/ flip--
1×+-commutative pow1/2 pow-prod-down associate-*l/ sum-log sqrt-prod distribute-lft-out distribute-lft-out--
Counts
4 → 87
Calls
4 calls:
102.0ms
(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0))) (+ (exp x) 1.0)))
19.0ms
(+ (exp x) 1.0)
37.0ms
(- (exp (* 2.0 x)) 1.0)
134.0ms
(- (exp (+ x x)) (* 1.0 1.0))

series346.0ms

Counts
4 → 12
Calls
4 calls:
245.0ms
(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0))) (+ (exp x) 1.0)))
17.0ms
(+ (exp x) 1.0)
45.0ms
(- (exp (* 2.0 x)) 1.0)
38.0ms
(- (exp (+ x x)) (* 1.0 1.0))

simplify1.9s

Counts
99 → 99
Iterations

Useful iterations: done (1.9s)

IterNodesCost
01831444
14611307
218111154
done50031098

prune792.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize62.0ms

Local error

Found 4 expressions with local error:

0.0b
(log1p (sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0))) (+ (exp x) 1.0))))
0.0b
(expm1 (log1p (sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0))) (+ (exp x) 1.0)))))
4.4b
(- (exp (* 2.0 x)) 1.0)
4.4b
(- (exp (+ x x)) (* 1.0 1.0))

rewrite160.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
15×*-un-lft-identity
13×add-cube-cbrt prod-diff
8×add-log-exp
7×fma-neg
5×expm1-log1p-u
4×pow1 add-exp-log add-cbrt-cube log1p-expm1-u
3×exp-sum difference-of-squares
2×sub-neg flip3-- diff-log flip--
1×log1p-udef expm1-log1p log1p-expm1 distribute-lft-out-- expm1-udef
Counts
4 → 74
Calls
4 calls:
1.0ms
(log1p (sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0))) (+ (exp x) 1.0))))
1.0ms
(expm1 (log1p (sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0))) (+ (exp x) 1.0)))))
30.0ms
(- (exp (* 2.0 x)) 1.0)
124.0ms
(- (exp (+ x x)) (* 1.0 1.0))

series1.2s

Counts
4 → 12
Calls
4 calls:
487.0ms
(log1p (sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0))) (+ (exp x) 1.0))))
640.0ms
(expm1 (log1p (sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0))) (+ (exp x) 1.0)))))
51.0ms
(- (exp (* 2.0 x)) 1.0)
36.0ms
(- (exp (+ x x)) (* 1.0 1.0))

simplify1.9s

Counts
86 → 86
Iterations

Useful iterations: done (1.9s)

IterNodesCost
01781624
14491495
217901263
done50001219

prune764.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize25.0ms

Local error

Found 2 expressions with local error:

0.0b
(fma 0.5 (pow x 2) (fma 1.0 x 2.0))
27.0b
(sqrt (fma 0.5 (pow x 2) (fma 1.0 x 2.0)))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt
3×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
2×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
1×rem-sqrt-square sqrt-pow1 pow1/2 fma-udef
Counts
2 → 25
Calls
2 calls:
1.0ms
(fma 0.5 (pow x 2) (fma 1.0 x 2.0))
3.0ms
(sqrt (fma 0.5 (pow x 2) (fma 1.0 x 2.0)))

series197.0ms

Counts
2 → 6
Calls
2 calls:
44.0ms
(fma 0.5 (pow x 2) (fma 1.0 x 2.0))
152.0ms
(sqrt (fma 0.5 (pow x 2) (fma 1.0 x 2.0)))

simplify3.3s

Counts
31 → 31
Iterations

Useful iterations: done (3.3s)

IterNodesCost
063451
1144414
2554377
33737369
done5000340

prune223.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes74.0ms

Accuracy

76.1% (0.7b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 3.1b

bsearch64.0ms

Steps
ItersRangePoint
5
-4.5846337071089676e-10
-2.188605173615867e-10
-4.5450129290399687e-10

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02435
12735
done2735

end0.0ms

sample10.0s

Algorithm
intervals
Results
5.4s6881×body10240exit
2.0s12981×body80nan
1.4s7412×body80valid
130.0ms717×body160valid