Details

sample5.7m (73.9%)

Algorithm
78×intervals
Results
4.3m34949×body10240exit
33.9s43795×body1280valid
10.9s30257×body640valid
7.3s203920×body80valid
4.6s152700×body80nan
4.5s27477×body320valid
3.0s36183×body160valid
2.9s173178×pre80true
726.0ms2945×body2560valid
360.0ms4117×pre10240exit
353.0ms7810×body160nan
95.0ms8409×pre80false
75.0ms221×body5120valid

prune50.5s (11.0%)

series38.6s (8.4%)

Calls

482 calls:

619.0ms
(expm1 (expm1 (log1p (log1p (* 0.5 (* s c_n))))))
585.0ms
(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))
447.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
360.0ms
(cbrt g)
329.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify13.1s (2.8%)

Algorithm
224×egg-herbie

regimes8.9s (1.9%)

Accuracy

Total 32.7b remaining (24.1%)

Threshold costs 5.6b (4.1%)

5.9b56.9%Cubic critical, narrow range
5.1b81.7%Quadratic roots, full range
4.9b30.7%Cubic critical, medium range
3.5b0%Cubic critical, wide range
3.2b71.3%Quotient of products

rewrite6.6s (1.4%)

Algorithm
146×rewrite-expression-head
Calls

482 calls:

333.0ms
(* (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
141.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
130.0ms
(sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
106.0ms
(* (- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0)) (/ 1 (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))
99.0ms
(- (/ (- 1.0) (pow x 2)) (+ (/ 3.0 x) (* 3.0 (/ 1 (pow x 3)))))
Rules
10386×*-un-lft-identity
8754×times-frac
8162×add-sqr-sqrt
6050×add-cube-cbrt
3270×prod-diff
2474×add-exp-log
1601×add-cbrt-cube
1265×distribute-lft-out
1128×sqrt-prod
967×associate-*r*
937×distribute-lft-out--
889×pow1
781×unpow-prod-down
778×difference-of-squares
776×div-exp
739×prod-exp
724×add-log-exp
698×distribute-rgt-neg-in
618×associate-/l*
587×distribute-lft-neg-in
583×div-inv
570×associate-/r/
502×associate-*l*
485×expm1-log1p-u
483×log1p-expm1-u
474×fma-neg
450×associate-/r*
388×cbrt-undiv
359×cbrt-prod
341×cbrt-unprod log-prod
309×pow-exp
263×flip-- fma-def
262×flip3--
259×flip-+
258×flip3-+
253×sqr-pow
244×cube-prod
228×pow-to-exp
215×unswap-sqr
193×neg-mul-1
162×unpow2
140×swap-sqr
136×pow-prod-down
116×clear-num frac-2neg
113×sqrt-div
101×associate-*r/
94×associate-/l/
90×*-commutative
76×sub-neg
75×pow-unpow
71×diff-log
63×distribute-rgt-in distribute-lft-in sqrt-pow1
62×unpow3 cube-mult
61×associate-*l/
57×frac-times cos-sum
56×sum-log
54×pow1/2 div-sub
52×log-pow
51×rem-sqrt-square
49×log-div
45×rec-exp 1-exp
39×pow1/3
36×+-commutative neg-sub0
35×rem-log-exp
32×exp-prod
30×pow-pow
29×cbrt-div
27×associate-+l+
24×frac-sub associate-+l-
23×sin-sum frac-add
22×neg-log
19×pow-flip
18×fma-udef sin-diff
16×tan-quot sin-mult associate--l+
15×cos-diff hypot-def pow-prod-up
14×distribute-rgt-out
13×sin-cos-mult pow-sqr
12×associate--l-
11×inv-pow distribute-frac-neg unpow-prod-up
10×acos-asin
9×pow-plus
8×pow2 associate-+r+ expm1-udef
6×rem-cube-cbrt acos-neg un-div-inv
5×expm1-log1p
4×associate-+r- distribute-rgt-neg-out
3×log1p-udef log1p-expm1 rem-cbrt-cube associate--r+
2×cube-div rem-exp-log distribute-lft1-in sqrt-unprod cos-mult distribute-rgt-out-- distribute-neg-frac
1×exp-diff sqrt-undiv sqrt-pow2 pow-sub unsub-neg rem-square-sqrt sub-div asin-acos exp-sum sum-cubes

localize2.3s (0.5%)

bsearch474.0ms (0.1%)

end1.0ms (0.0%)